An explicit formula for the \(A\)-polynomial of the knot with Conway's notation \(C(2n,4)\) (Q2679804)

The \(A\)-polynomial of a knot in the \(3\)-sphere \(S^3\) was introduced in the 90's [\textit{D. Cooper} et al., Invent. Math. 118, No. 1, 47--84 (1994; Zbl 0842.57013)]. It describes the \(\mathrm{SL}_2(\mathbb{C})\)-character variety of the knot complement as viewed from the boundary torus. The \(A\)-polynomial carries a lot of information about the topology of the knot. However, finding an explicit formula for the \(A\)-polynomial is a challenging problem. So far, the \(A\)-polynomial has been computed only for a few classes of knots. In this paper, the authors give an explicit formula for the \(A\)-polynomial of the knot having Conway's notation \(C(2n,4)\) up to repeated factors.